Let's solve this problem step by step.
FIRST. <em>Quadrilateral A′B′C′D′ is obtained by a reflection across the y-axis of quadrilateral ABCD</em>
When we reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate changes in sign. So:
(x, y) → (-x, y)
SECOND. <em>Followed by a translation 3 units to the left and 3 units down.</em>
To translate a point <em>3 units to the left</em> subtract 3 from the x-coordinate and to translate a point <em>3 units down </em>subtract 3 from the y-coordinate. Therefore, the function we are looking for is:
f(x, y) = (-x - 3, y - 3)
Answer:


And using a calculator, excel ir the normal standard table we have that:

And we can calculate the probability like this:
Step-by-step explanation:
A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and 
Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:

We can find the probability required like this:


And using a calculator, excel ir the normal standard table we have that:

And we can calculate the probability like this:

Answer:
50, 60, 70: More than one triangle
60, 15, 15: A unique triangle
80m, 65m, 20m: No triangle
Since:
Density=Mass/Volume
Mass=Volume*Density
Therefore, Volume=Mass/Density
Consider this option (see the attachment).
If it is possible, check it in other sources.